@avi - Nope, never heard Dror Yikra sung to that tune. I guess we live in different parts of town... :)
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DaveJul 11 '11 at 17:52

A rabbi of mine told me the following in the name of Rabbi Nachman from Breslov: Only on shabbat do gentile melodies become holy. Mah she'ein ken regarding Jewish songs that are holy the entire week all seven days including shabbat.
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Adam MoshehApr 17 '12 at 18:54

10 Answers
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Two popular Chabad Chassidic niggunim were both adapted from French songs:

"Napoleon's March," taken from the marching tune used by the French army during their invasion of Russia in 1812. (R' Shneur Zalman is said to have heard the tune and said that it represents the ultimate victory of "our" - the Russian - side, as indeed occurred.)

"Ha'aderes Veha'emunah," set in 1973 by some French chassidim to the tune of La Marseillaise. (Interestingly, a few months later the French government formally altered the tune - their national anthem - somewhat. In a talk of his in 1991, the Lubavitcher Rebbe zt"l observed that evidently, on a spiritual level, they realized that the original tune no longer "belonged" to them.)

Well, the traditional Ashkenazic "Maoz Tzur" would be a great candidate since it is in perfect cadence and key with "Deck the Halls". The problem is that Maoz Tzur (the Ashkenazic tune) is actually a knock-off of a German folk tune! See here and here.
As per the wiki article it actually was chosen by Luther sr"y for one of his hymns. What is still amazing is the similarity between Maoz Tzur, being of German origin and Deck the Halls, being of Welsh origin.